I have emailed to me@onenote.com and the note appears in the Quick Notes Section of the default Notebook on Onedrive.
I have the 'cache' copy of the notebook open in 2013 but the note does not appear unless I manually sync.
The setting for sync is set to automatic, sync on changes.

You are not expecting to much but it takes a couple of minutes. I use me@onenote all the time and it works perfectly. I never sync manually and see all my request coming in and appear on the Quick Notes tab. As i said takes a couple of minutes after you pressed send.

Thank you for taking the time to reply. It is not what happens here.
I have Android Tablet showing default web notebook, PC showing the same and have Onedrive open in browser.
When I send the email it appears within a minute in the browser.
The android will display it if I change page and back, I didn't wait more than 5 minutes.
The PC after waiting 10-15 minutes then only shows it if I click in another notebook and back or click sync now.

If it should happen on its own there must surely be something wrong. The broadband and wireless are working fine to Android and the PC is on Ethernet to the same router.
Must the connection be wireless to the PC to work? [Edit] No that is not sensible.

The problem with the desktop onenote is solved by running reset Onedrive from the Help in the taskbar.
It does not solve the Android side which requires a touch on a different page and back to trigger it.

[EDIT] Red herring, it did solve the emails immediately updating desktop but did not reflect page deletions without triggering sync manually.